It's interesting to note that it isn't working-class people—the people who might reasonably feel threatened—who are demanding "safe spaces". It's extremely privileged people educated in elite institutions. These are some of the most privileged people alive with advantages not accessible to the vast majority of the population of any ethnicity or race.
In the specific story the OP linked to (about college students) that's true. But I don't think that automatically means working class people are not demanding similar spaces for themselves. Can you be sure they aren't?